Scalar quasinormal and quasibound states of weakly magnetized Ernst--Schwarzschild spacetime: a confluent-Heun Wronskian approach

@misc{ferreira2026scalar,
  title = {{Scalar quasinormal and quasibound states of weakly magnetized Ernst--Schwarzschild spacetime: a confluent-Heun Wronskian approach}},
  author = {Danilo S. Ferreira and Luis B. Castro},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17727},
  eprint = {2609.17727},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17727},
}

TY  - UNPB
TI  - Scalar quasinormal and quasibound states of weakly magnetized Ernst--Schwarzschild spacetime: a confluent-Heun Wronskian approach
AU  - Danilo S. Ferreira
AU  - Luis B. Castro
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17727
UR  - https://arxiv.org/abs/2609.17727
AB  - We study the quasinormal-mode and quasibound-state spectra of a massless scalar field in weakly magnetized Ernst--Schwarzschild spacetime. In the separated O(B_0^2) regime, the Klein--Gordon equation reduces to a radial confluent-Heun equation. We construct an endpoint-selected spectral Wronskian directly from the canonical confluent-Heun recurrence and its regular-to-irregular connection limit. Quasinormal modes and quasibound states are then obtained as zeros of the same analytic spectral function on the radiative and bound sheets, respectively, providing a unified treatment of the two spectral sectors within the separated weak-field problem. The resulting QNM and QBS frequencies agree with independent weak-field Ernst and massive-Schwarzschild benchmarks available in the literature. We further show, for representative cases, that the frequencies selected by the local Heun-series termination relation examined here do not satisfy the endpoint-selected quasibound-state condition. The construction therefore provides a direct horizon-to-infinity spectral condition for both radiative and bound states within the weak-field Ernst problem.
ER  -